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I'm interested in studying the prime spiral interactively.

This question talks about some interesting patterns in the spiral involving quadratic equations. The idea I had was, write a program that outputs all values of a polynomial for a certain domain, output values to a list, and check for elements in common with another list, based on another polynomial of that same form. I'd want to make some plots.

What's a good way to play around this using an interpreter? I've never used Octave. Is that the kind of thing it's good for? Or Sage?

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Octave's a bit more suitable for computations involving inexact arithmetic. For number-theoretic investigations, you'd want a system that can do exact integer/rational arithmetic, like Maple or Mathematica. Sage can do exact arithmetic, I'm told, but I've no experience with it. –  J. M. Nov 30 '11 at 1:42
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